论文标题
无限层的可代表性层；某些圆柱代数比其他代数更为代表
An infinite stratum of representability; some cylindric algebras are more representable than others
论文作者
论文摘要
令$ 2 <n <m \ leqω$。令$ \ ca_n $表示尺寸$ n $和$ \ rca_n $的圆柱代数的类，表示代表$ \ ca_n $ s的类。我们说，如果$ \ cm \ at \ at \ a $具有$ m $ -square表示形式，则$ \ a \ in \ rca_n $最高为$ m $。 $ m $ $ square代表是本地相关的代表，它仅在所谓的$ m $ -squares'上是当地的。大致是我们通过可移动窗口放大到$ m $ $ $方形的表示形式，将成为确定的一点，并且取决于$ m $，在这些窗口中，我们将$ m $ $ $ square-eprentation误认为是真正的经典。当我们缩小不可支配的部分时，会变得更加暴露。对于$ 2 <n <m <l \leqΩ$，$ l $ square代表为$ m $ -square;但是，匡威是不正确的。品种$ \ rca_n $是一个有限的案例，与$ \ ca_n $ s具有$ω$ -SQUARE表示。令$ \ rca_n^m $为代表的代数最多可达$ m $。我们表明$ \ rca_n^{m+1} \ subsetneq \ bold \ rca_n^m $ for $ m \ geq n+2 $。
Let $2<n<m\leq ω$. Let $\CA_n$ denote the class of cylindric algebras of dimension $n$ and $\RCA_n$ denote the class of representable $\CA_n$s. We say that $\A\in \RCA_n$ is representable up to $m$ if $\Cm\At\A$ has an $m$-square representation. An $m$ square represenation is locally relativized represenation that is classical locally only on so called $m$-squares'. Roughly if we zoom in by a movable window to an $m$ square representation, there will become a point determinded and depending on $m$ where we mistake the $m$ square-representation for a genuine classical one. When we zoom out the non-representable part gets more exposed. For $2<n<m<l\leq ω$, an $l$ square represenation is $m$-square; the converse however is not true. The variety $\RCA_n$ is a limiting case coinciding with $\CA_n$s having $ω$-square representations. Let $\RCA_n^m$ be the class of algebras representable up to $m$. We show that $\RCA_n^{m+1}\subsetneq \bold \RCA_n^m$ for $m\geq n+2$.
